Cointegration by Parts: Locating Cointegration in Time
Abstract
Tests for cointegration are typically applied to a single window spanning the entire sample, assuming that the long-run relationship holds throughout. When it holds over only a part of the sample, such tests lose power, because the stationary episode is diluted by periods without cointegration. We propose three statistics for testing whether two or more series cointegrate only over a part of the sample, each an infimum of the Engle-Granger statistic over recursive, backward-expanding, or doubly-flexible windows. We derive their limiting distributions and establish which alternatives each is consistent against. Only the doubly-flexible statistic has power against both break directions. Inspired by the seminal work of James G. MacKinnon, critical values are obtained by simulation and summarized through response surface regressions. We apply the tests to global mean sea level and global mean surface temperature anomalies. All three reject the null of no cointegration at the 5% level, locating it in a sub-period of the 1880--2019 record that coincides with documented discontinuities in sea surface temperature data collection.
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BibTeX
@misc{kvist2026cointegration,
title = {{Cointegration by Parts: Locating Cointegration in Time}},
author = {Olivia Kvist and J. Eduardo Vera-Valdés},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10020},
eprint = {2609.10020},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10020},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cointegration by Parts: Locating Cointegration in Time
AU - Olivia Kvist
AU - J. Eduardo Vera-Valdés
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10020
UR - https://arxiv.org/abs/2609.10020
AB - Tests for cointegration are typically applied to a single window spanning the entire sample, assuming that the long-run relationship holds throughout. When it holds over only a part of the sample, such tests lose power, because the stationary episode is diluted by periods without cointegration. We propose three statistics for testing whether two or more series cointegrate only over a part of the sample, each an infimum of the Engle-Granger statistic over recursive, backward-expanding, or doubly-flexible windows. We derive their limiting distributions and establish which alternatives each is consistent against. Only the doubly-flexible statistic has power against both break directions. Inspired by the seminal work of James G. MacKinnon, critical values are obtained by simulation and summarized through response surface regressions. We apply the tests to global mean sea level and global mean surface temperature anomalies. All three reject the null of no cointegration at the 5% level, locating it in a sub-period of the 1880--2019 record that coincides with documented discontinuities in sea surface temperature data collection.
ER -